Highlighting text will allow you to copy, and searching the page will showcase results for the phrase entered. There doesn’t seem to be any difference in the viewer from one document to another.

This is a command line application that quickly converts any PDF file into a PDF/A file complete with optical character recognition, meaning you'll be able to search the text.

If you want to extract highlighted text from PDF file as a plain text file, then this post covers some good free PDF Highlight Extractor software to do that.